text: The Landau equation is linear when it is written for the dependent variable ,
  The general solution for  of the above equation is
  As , the magnitude of the disturbance  approaches a constant value that is independent of its initial value, i.e.,  when . The above solution implies that  does not have a real solution if  and . The associated solution for the phase function  is given by
  As , the phase varies linearly with time, 
  It is instructive to consider a hydrodynamic stability case where it is found that, according to the linear stability analysis, the flow is stable when  and unstable otherwise, where  is the Reynolds number and the  is the critical Reynolds number; a familiar example that is applicable here is the critical Reynolds number, , corresponding to the transition to Kármán vortex street in the problem of flow past a cylinder. The growth rate  is negative when  and is positive when  and therefore in the neighbourhood , it may written as  wherein the constant is positive. Thus, the limiting amplitude is given by